Every colour is a point at the intersection of 3 lines. But every colour can also be viewed in the context of 3 intersecting 2-dimensional planes. Want to learn more about where a colour is in the 3D colour space? Take a look at colour by the slice . . .

As we explored in the previous 'Leap' lesson, every Colour Card in the BTC deck has a place along 3 different axis lines. And as we learned in Colour Geometry, a Line takes us through a single dimension, from one point to another in one direction and back again, in one of three planes in space: left to right, forwards and backwards, up and down.

Think about moving through a house: a hallway can take you from the front of the house to the back; you can turn left or right from that hallway to enter rooms on one side of the house or the other; and you can go up or down the stairs to get to the basement, the second floor, or the attic. In the BTC 'house' you can also move through the space, front to back, left to right, and up and down. With 6 possible steps in each direction, these 6-step colour flows can be identified by shifting each of the 3 element primary colours one at a time through their full range from 0 to 5.

Every BTC colour has a place along 3 different 1-dimensional axis lines of 6 (and they all intersect each other at that colour), and every colour has a place within 3 different 2-dimensional planes of 6 x 6, as 1 of 36 different colours with the same amount of each element primary ingredient. Picture the 6 x 6 x 6 BTC Colour Cube as a block that can be sliced into 6 like a loaf of bread, or layered like a 6-layer cake from bottom to top, or wandered through like the hallways, rooms, and floors of a 6-storey house.

Here's what the BTC Colour Cube would look like, slice by slice, showing each of the 3 element primary colours in their different amounts from 0 (none) to 5 (full strength):

Each of the 3 element primary ingredients (Cyan, Yellow, and Magenta) shifts through the 3D colour space along a different axis plane, front to back, top to bottom, left to right.

You can do the same with the simpler 3 x 3 x 3 Colour Basics Colour Cube, showing only Cyan, only Yellow, and only Magenta, in their none, half, and full-strength slices:

In each of the monochromatic cubes above (both the 6 x 6 x 6s and the 3 x 3 x 3s), we see the White Corner front and centre. Because it has 0 Cyan, 0 Magenta, and 0 Yellow, that unit Cube is White, no matter how you slice it.

THE LINES OF 205

We know there is only 1 Colour Card for every different 3-digit Colour Code. In the previous 'Leap' we looked at 205, a pure Hue from the Yellow family, and we saw it as part of 3 different straight flows of 6: one showed us the Hue between its 'parent' Corner Colours (Yellow and Green); one showed us the Hue losing itself towards the White Corner; and one showed us how adding Magenta can turn a Yellow (even a Green-Yellow) into a Red. Rotating the BTC Colour Cube to show the Yellow Corner at the centre (and including the other Corner Colours for reference), here's what all 3 of those 1-dimensional Lines look like, intersecting together in one specific XYZ/CMY place to create that one specific colour:

342, SLICE BY SLICE BY SLICE

To see how a single colour fits into the Colour Cube 'slice by slice,' we're going to go inside the colour space and look at a Tone. This is 342:

It has a Cyan value of 3 (more than half), a Magenta value of 4 (also more than half), and a Yellow value of 2 (and here, the Yellow isn't really Yellow, but rather a part of Black). Looking at the Saturation Summary (as part of the Code Side on the left), you can see that all this adds up to a Base Hue that is half Blue and half Magenta (there's a Colour Basics Connector Hue card for that one...). It also has some Black and some White (more Black than White, making the Grey a darker Grey). Hue plus Black plus White means it's a Tone, so it's hidden within the core of the Colour Cube.

It's good to picture the 216 Colour Cube as a single unit, keeping all the individual colours in their places relative to one another. But as mentioned earlier, you can also think of it as a block that can be sliced vertically (left to right, or front to back), or horizontally (top to bottom). Doing that, we can picture our hidden Tone as an intersection of 3 different 6 x 6 slices. Keeping the same orientation as the Cube above (showing 3 Lines intersecting on the outside at 205), here are the 3 2-dimensional planes that intersect inside the Cube at 342:

It's hard to show all 3 slices all at once at their XYZ/CMY meeting point, and you can't actually 'slice' a BTC Colour Cube into layers. But you can create all 3 slices by arranging your Colour Cards into 3 different 6 x 6 grids, one for each of the C, M, and Y values...

CYAN AT 3

Here is 342 in a 6 x 6 grid layer with all the other colours that have a Cyan value of 3:

These 36 colours show a broad gamut, but they all have the same amount of Cyan. In the top left corner, we see 300, which is Cyan at 3, and nothing else. In the bottom right corner, there's still Cyan at 3, but it's overpowered by Red (Magenta + Yellow) at a full 5, so it's no longer really Cyan as a Hue factor, but more the missing third of Black, turning full pure Red (055) into a Shade of Red in the Black family.

Going from left to right, the columns show an increase of Magenta; the middle digit in the Colour Code increases from 0 in the left column to 5 in the right column. Going from top to bottom, the rows show an increase in Yellow; the last digit in the Colour Code increases from 0 in the top row to 5 in the bottom row.

C3 PALETTE

Note that the first digit (the Cyan digit) is '3' in all these samples.

Choosing a common element primary ingredient at a specific quantity can be a subtle way to create a cohesive colour palette, even if that ingredient gets mixed together with more dominant other parts. In more practical terms, adding the same single colour to a bunch of other different colours can unify an unrelated collection into a group with something in common.

MAGENTA AT 4

Here is 342 in a 6 x 6 grid layer with all the other colours that have a Magenta value of 4:

All of the colours in this 6 x 6 layer have the same amount of Magenta. In the top left corner, you can see Magenta by itself as 040. In the opposite bottom right corner, the Magenta is serving as a third of Black, to turn pure Green (505) into an almost-Black Shade of Green.

Going from left to right, the columns show an increase of Yellow; the last digit in the Colour Code increases from 0 in the left column to 5 in the right column. Going from top to bottom, the rows show an increase in Cyan; the first digit in the Colour Code increases from 0 in the top row to 5 in the bottom row.

M4 PALETTE

Note that the middle digit (the Magenta digit) is '4' in all these samples.

Magenta is the strongest of the element primary Hues, so having it as a constant ingredient at an almost full 4 out of 5, it's going to create a palette that looks more often like Magenta and less like the other element primary ingredients, even though only 9 out of the 36 M4 colours are actually in the Magenta family.

YELLOW AT 2

Here is 342 in a 6 x 6 grid layer with all the other colours that have a Yellow value of 2:

With a 'less than half' value of only 2, Yellow is the least significant element primary ingredient in our featured colour 342. All it's really doing is adding Black. We can see it as a light Tint in the top left corner (part of the White family), but as the weakest of the Corner Hues, it loses its identity pretty quickly as Cyan moves in on the columns to its right, and Magenta gets added in the rows below.

Going from left to right, the columns show an increase of Cyan; the first digit in the Colour Code increases from 0 in the left column to 5 in the right column. Going from top to bottom, the rows show an increase in Magenta; the middle digit in the Colour Code increases from 0 in the top row to 5 in the bottom row.

I find that seeing a single colour as part of each of the 3 layers of its individual element primary ingredients helps to see how that ingredient influences the colour as a sum of its parts.

Y2 PALETTE

Note that the last digit (the Yellow digit) is '2' in all these samples.

Yellow is the weakest of the element primary ingredients, and 2 is less than half, so in most of the Y2 colours, the Yellow barely reads. Still, it's surprising how a common ingredient at a constant quantity can bring colours together, even in subtle ways.

COLOUR LAB

This is an exercise I call 'Layer Up.' All 216 BTC Colour Cards can be layered out in 3 different 6 x 6 x 6 grids, with columns of one element primary, rows of another, and layers of the third. For example, to 'Layer Up' with Cyan, start with the 36 BTC Colour Cards that have no Cyan at all, whose Colour Codes start with 0. Arrange them in a 6 x 6 grid, beginning with the 4 'no Cyan' Corner Colours (White, Magenta, Yellow, and Red) in the 4 corners:

Connect the Corners by completing the 4 edges of the 6 x 6 square grid: White across to Magenta, White down to Yellow, Magenta down to Red, and Yellow across to Red:

Fill in the rest of the grid. Magenta (the middle digit in the Colour Code) increases in the columns from 0 in the left column to 5 in the right column. Yellow (the last digit in the Colour Code) increases in rows from 0 in the top row to 5 in the bottom row. Once you have all the Cyan=0 cards in place, your grid will look like this:

You now have the first layer of your 3D grid complete, using all 36 cards in the deck that have no Cyan at all.To 'Layer Up' and begin to add to the grid in height, find all 36 Colour Cards that start with a 1, that have a Cyan value of 1. Stack them in a second layer on the grid of Cyan=0 cards, according to the same Magenta columns and Yellow rows you defined in the first layer of the grid, like this:

In the Magenta and Yellow digits, this second layer Colour Codes are exactly the same as the first; all that's changed is the Cyan digit, increasing from 0 to 1. You can see how even this small amount of Cyan is influencing the whole layer, adding a wash of Cyan across the whole gamut.Can you keep going, adding each layer of 36 cards as the amount of Cyan increases? In the third layer, all the cards will start with 2, then 3, then 4... By the time you get to the final 36 Colour Cards (all with a Cyan value of 5) you will complete your 6 x 6 x 6 grid with the remaining 4 Corner Colour Cards (Cyan, Blue, Green, and Black) in the 4 corners of the top layer.

In the first 3 layers, where Cyan is less than half (C0, C1, and C2), the cards will come from the White, Magenta, Yellow, and Red families. In the layers where Cyan is more than half (C3, C4, or C5), the cards will come from the Cyan, Blue, Green, and Black families. Most of the colours in the top 3 layers will look like they belong within the Cyan gamut (as Cyan family colours, or Blue and Green family colours). But remember, Cyan may also be present in a colour not on its own, but as part of Black (C+M+Y) so the Cyan may not be apparent as an individual ingredient in the colour.

COLOUR LAB

Once you've sorted out all 216 BTC Colour Cards with Cyan as the 'Layer Up' ingredient, try the exercise again with a different arrangement of columns, rows, and layers. To 'Layer Up' with Magenta, start with the 36 cards that have a middle digit of 0 (no Magenta). To 'Layer Up' with Yellow, start with the 36 cards that have a last digit of 0 (no Yellow).

'LAYER UP' WITH COLOUR BASICS

If you want to try a simpler version of 'Layer Up,' you can use the 27 Corner and Connector Cards in the Colour Basics deck. For example, to Layer Up with Cyan, find the 9 cards that have no Cyan, and make a 3 x 3 grid that has Magenta increasing in columns left to right and Yellow increasing in rows top to bottom. Then 'Layer Up' with the 9 cards that add half Cyan to the first layer grid, and then complete the grid with the 9 cards that add full Cyan:

Using the Colour Basics cards, you have fewer cards to have to keep track of, but you may actually find it easier to see the colours shifting from none to full when there are more steps between the Corners.

You may also find it easier to create the grids by building your layers using the Code Side, referencing the Hue Matrix, rather than referencing the 3-digit Colour Code on the Colour Side. Or try both, and see which works better for you and how you see patterns: numerically with the Colour Codes, or visually with the Hue Matrix. Before you know it, you'll be able to 'Level Up' without looking at the codes at all.

NEXT 'LEAP' >>

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